Scholze showed in [1]} that the construction of projectivoid space is compatible with the tilting functor. In this section we begin our exploration of so called projectivoid geometry by developing the theory of line bundles on projectivoid space. In particular, we compute the Picard group of \(^{n,}\) , as well as the sheaf cohomology of all line bundles. We continue developing the theory in the following section, where we will show how an arbitrary perfectoid space's maps to projectivoid space is intimately connected to its theory of line bundles, reflecting the situation in classical algebraic geometry, but with an extra arithmetic twist.
